Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
386 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#15667947 | C2 | semidirect |
| 3. #26019010 | C2 | semidirect |
| 6. #26018143 | C2 | semidirect |
| 7. C89×#1299 | C2 | semidirect |
| 181. #1299 | D89 | semidirect |
| 182. C89 | #8673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029213 | 2 |
| C4×#15667947 | 2 |
| #26019010 | 2 |
| #26018692 | 2 |
| #26018689 | 2 |
| #26018143 | 2 |
| C89×#1299 | 2 |
| #8673 | 89 |